Weight Painting - Stiff vs Flexible Deformation
What you're missing is another bone for the last horizontal part of the mesh, which will act as a "balance". In Blender Weights are always normalized, to distribute the movements between deforming bones, but if a vertex is weighted to one bone only, the normalization is calculated between a weight and zero: so a weight of 0.0001 and a weight of full 1.0 are treated the same way (both values are infinitely larger than zero).

The vertices in your "green zone" are affected by two bones, which blend their action, while the vertices in the "red zone" are affected by one bone only, leading to a "rigid" behaviour.